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For comparison against images of real structures, it is quite useful to be able to produce simulated
TEM and other types of images of structures existing only within the computer. To simulate a
TEM image, one selects a given thickness section of the three-dimensional continuum structure,
digitizes it into a 3-D image (cubic array, J(x,y,z), typically 256 on a side), and simply sets the
intensity of each pixel in the simulated TEM image according to:
where J(x,y,z) is equal to 1 for pixels digitized as solids and 0 for pixels digitized as porosity and
f(x) is an arbitrary weighting function taken as equal to one in the examples provided in this
paper. Figure 1 shows a computer simulated TEM image for the macrostructure of the model C-
S-H gel. To compare against real TEM images, it is of interest to superimpose the sub-nanometer
level texture of the gel onto this macro image. This can be approximately achieved by generating
a TEM at the tenths of nanometers scale, rescaling it to match the scale of the macro image, and
using a maximum operation (at each pixel, the resultant image is composed of the maximum
greylevel present in the two component images) to combine the two images. These operations
can be achieved easily on most conventional image processing systems.
One can also simulate atomic force microscopy images using these same principles. Here, after
the 3-D digitization, the 2-D image intensities are computed as:
where min [z:J(x,y,z)=1] indicates the depth in the sample at which solid material is first
encountered and the value is subtracted from C (e.g., 255 for an 8-bit greylevel representation) to
obtain the desired effect that solids closer to the surface in contact with the AFM tip (z=0) are
brighter. Figure 2 shows a simulated AFM image for the micro-level structure of the model C-S-
H. The ability to produce such images allows a direct comparison to be made between the
computer model and the real material, as will be illustrated for TEM images in the results section.
Figure 1. Simulated TEM image of the macro-level model C-S-H structure.
Complete image is 250 nm by 250 nm and section is 25 nm thick.
Figure 2. Simulated AFM image of the micro-level model C-S-H structure.
Complete image is 25 nm by 25 nm.
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